Related papers: A Simple One-Electron Expression for Electron Rota…
The problem of construction of the Wannier functions (WFs) in a restricted Hilbert space of eigenstates of the one-electron Hamiltonian $\hat{H}$ (forming the so-called low-energy part of the spectrum) can be formulated in several different…
We propose an efficient basis expansion for electron orbitals to describe real-time electron dynamics in crystalline solids. Although a conventional grid representation in the three-dimensional Cartesian coordinates works robustly, it…
We present an alternative one-electron equation for resolving many-electron problem to one-electron approximation and including the exchange and correlation effects in an analytical way, thereby fulfilling the requirements for ab initio…
A possibility to perform single-electron computing without dissipation in the array of tunnel-coupled quantum dots is studied theoretically, taking the spin gate NOT (inverter) as an example. It is shown that the logical operation can be…
We calculate within a semiclassical approximation the autocorrelation function of cross sections. The starting point is the semiclassical expression for the diagonal matrix elements of an operator. For general operators with a smooth…
Matrix elements of spherical tensor operators are fundamental to the analysis of lanthanide spectra in both amorphous and crystalline host materials. In the intermediate coupling scheme, the eigenvectors of the Hamiltonian define the…
Quadratic operators are used in transforming the model Hamiltonian (H) of one correlated and dispersive band in an unique positive semidefinite form coopting both the kinetic and interacting part of H. The expression is used in deducing…
An efficient computational algorithm to implement a local operator approach to partitioning electronic energy in general molecular systems is presented. This approach, which rigorously defines the electronic energy on any subsystem within a…
An analytical expression for the supercurrent of a superconducting single-electron transistor (SSET) is derived. The derivation is based on analogy between the model Hamiltonian for E_J>E_C and a discrete, one-dimensional harmonic…
We analyse a path to construct density functionals for the dispersion interaction energy from an expression in terms of the ground state densities and exchange-correlation holes of the isolated fragments. The expression is based on a…
Spatially localized one-electron orbitals, orthogonal and nonorthogonal, are widely used in electronic structure theory to describe chemical bonding and speed up calculations. In order to avoid linear dependencies of localized orbitals, the…
Suzuki-Trotter decompositions of exponential operators like $\exp(Ht)$ are required in almost every branch of numerical physics. Often the exponent under consideration has to be split into more than two operators $H=\sum_k A_k$, for…
We propose a scheme for investigating the quantum dynamics of interacting electron models by means of time-dependent variational principle and spin coherent states of space lattice operators. We apply such a scheme to the one-dimensional…
Kjolstad et. al. proposed a tensor algebra compiler. It takes expressions that define a tensor element-wise, such as $f_{ij}(a,b,c,d) = \exp\left[-\sum_{k=0}^4 \left((a_{ik}+b_{jk})^2\, c_{ii} + d_{i+k}^3 \right) \right]$, and generates the…
We show that a rectangular collocation method, equivalent to evaluating all matrix elements with a quadrature-like scheme and using more points than basis functions, is an effective approach for solving the electronic Schr\"odinger equation…
In this paper we derive general expressions for few-electron spectral functions of the one-dimensional Hubbard model for values of the excitation energy in the vicinity of the $M^{th}$ upper-Hubbard band lower limit. Here $M=1,2,...$ is the…
The problem of motion of a single electron interacting with a periodic lattice of two-level systems is investigated within a spinless fermion model. The Green's function is calculated in a single-site dynamical coherent potential…
A recently proposed method of continuous unitary transformations is used to eliminate the interaction between electrons and phonons. The differential equations for the couplings represent an infinitesimal formulation of a sequence of…
Extracting molecular properties from a wave function can be done through the linear response (LR) formalism or, equivalently, the equation of motion (EOM) formalism. For a simple model system, He in a 6-31G basis, it is here shown that…
The molecular Schr\"odinger equation is rewritten in terms of non-unitary equations of motion for the nuclei (or electrons) that depend parametrically on the configuration of an ensemble of generally defined electronic (or nuclear)…